YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
*(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
+(*(x:S,y:S),*(a,y:S)) -> *(+(x:S,a),y:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
-> Rules:
 *(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
 +(*(x:S,y:S),*(a,y:S)) -> *(+(x:S,a),y:S)

Problem 1: 

SCC Processor:
-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
-> Rules:
 *(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
 +(*(x:S,y:S),*(a,y:S)) -> *(+(x:S,a),y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
->->-> Rules:
 *(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
 +(*(x:S,y:S),*(a,y:S)) -> *(+(x:S,a),y:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
-> Rules:
 *(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
 +(*(x:S,y:S),*(a,y:S)) -> *(+(x:S,a),y:S)
->Projection:
 pi(*#) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
 +(*(x:S,y:S),*(a,y:S)) -> *(+(x:S,a),y:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.